In this paper, we give the first relationally parametric model of
the (extensional) calculus of constructions. Our model remains as
simple as traditional PER models of dependent types, but unlike
them, our model additionally permits relating terms at
different implementation types. Using this model, we can
validate the soundness of quotient types, as well as derive strong
equality axioms for Church-encoded data, such as the eta-law for
strong dependent pair types.

Insofar as anything having to do with dependent types can be, the key idea in this paper is really, really simple. There's a really beautiful, simple generalization of partial equivalence relations (aka PERs) (called quasi-PERs) that let us give a parametric model without having to jump through the hoops the usual methods does.